Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/6` and the angle between sides B and C is `pi/12`. If side B has a length of 12, what is the area of the triangle?

Answer 1

Angle C is `pi/6` and angle A is `pi/12`. Hence angle B= `pi-pi/6-pi/12= (3pi)/4`

Side b =12 , therefore using the formula `sinA/a= SinB/b`

it would be side a= b sinA/ SinB= `12 sin (pi/12)/sin((3pi)/4)`

For area of triangle use the formula `1/2 ab sinC`

=`(1/2)12(12) sin (pi/12)/sin((3pi)/4) sin (pi/6)`

= `72(0.2588)(0.5)/0.7071`

=13.176